Non-linear reference line optimization method using piecewise quintic polynomial spiral paths for operating autonomous driving vehicles

ABSTRACT

A first reference line representing a trajectory from a first location to a second location associated with an autonomous driving vehicle (ADV) is received. The first reference line is segmented into a number of reference line segments. For each of the reference line segments, a quintic polynomial function is defined to represent the reference line segment. An objective function is determined based on the quintic polynomial functions of the reference line segments. An optimization is performed on coefficients of the quintic polynomial functions in view of a set of constraints associated with the reference line segments, such that an output of the objective function reaches minimum while the constraints are satisfied. A second reference line is then generated based on the optimized parameters or coefficients of the quintic polynomial functions of the objective function. The second reference line is then utilized to plan and control the ADV.

TECHNICAL FIELD

Embodiments of the present disclosure relate generally to operatingautonomous driving vehicles. More particularly, embodiments of thedisclosure relate to generating reference lines of trajectories foroperating autonomous driving vehicles.

BACKGROUND

Vehicles operating in an autonomous mode (e.g., driverless) can relieveoccupants, especially the driver, from some driving-relatedresponsibilities. When operating in an autonomous mode, the vehicle cannavigate to various locations using onboard sensors, allowing thevehicle to travel with minimal human interaction or in some caseswithout any passengers.

Motion planning and control are critical operations in autonomousdriving. Particularly, trajectory planning is a critical component in anautonomous driving system. Conventional trajectory planning techniquesrely heavily on high-quality reference lines, which are guidance paths,e.g., a center line of a road, for autonomous driving vehicles, togenerate stable trajectories. Usually, the map data (typically asequence of two-dimensional (2D) points in the world frame) directlyfrom sensors cannot provide the required smoothness, and thereforedirectly using the map data may cause the planners generating unstableand oscillating trajectories between planning cycles.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure are illustrated by way of example and notlimitation in the figures of the accompanying drawings in which likereferences indicate similar elements.

FIG. 1 is a block diagram illustrating a networked system according toone embodiment.

FIG. 2 is a block diagram illustrating an example of an autonomousvehicle according to one embodiment.

FIGS. 3A-3B are block diagrams illustrating an example of a perceptionand planning system used with an autonomous vehicle according to oneembodiment.

FIG. 4 is a block diagram illustrating an example of a planning moduleaccording to one embodiment.

FIG. 5 shows a reference line segmented into a number of reference linesegments according to one embodiment.

FIG. 6 shows a reference line segment further segmented into a number ofsub-segments according to one embodiment.

FIG. 7 shows an original reference line and an optimized reference lineaccording to one embodiment.

FIG. 8 is a flow diagram illustrating an example of process foroptimizing a reference line according to one embodiment.

FIG. 9 is a block diagram illustrating a data processing systemaccording to one embodiment.

DETAILED DESCRIPTION

Various embodiments and aspects of the disclosures will be describedwith reference to details discussed below, and the accompanying drawingswill illustrate the various embodiments. The following description anddrawings are illustrative of the disclosure and are not to be construedas limiting the disclosure. Numerous specific details are described toprovide a thorough understanding of various embodiments of the presentdisclosure. However, in certain instances, well-known or conventionaldetails are not described in order to provide a concise discussion ofembodiments of the present disclosures.

Reference in the specification to “one embodiment” or “an embodiment”means that a particular feature, structure, or characteristic describedin conjunction with the embodiment can be included in at least oneembodiment of the disclosure. The appearances of the phrase “in oneembodiment” in various places in the specification do not necessarilyall refer to the same embodiment.

According to some embodiments, a new constrained numerical optimizationmethod is utilized that takes the map data in a format of a sequence of2D points and generates a smooth and piecewise concatenated referenceline with minimal curvature changes. Given a sequence of 2D points, thesystem first connects consecutive points using arbitrary quinticpolynomial spiral paths. By perturbing these piecewise paths, theoptimization system finds a best set of these paths that have theoverall minimal curvature changes, and are smoothly connected at thejoint points up to the third derivative, in an iterative fashion.

The quintic polynomial spiral paths are utilized as piecewise paths tosimplify the objective formulation. The objective of the optimization isto minimize the overall curvature changes along the reference line.However, it is extremely complex to formulate the objective if thepiecewise paths are defined in world frames (e.g., in Cartesian space).To solve the problem, spiral paths, i.e., the curve direction isfunction of curve length, are utilized as piecewise paths, and thereforethe objective can be easily formulated. The coordinates of the points inthe spiral path can be computed using numerical integration. Inaddition, users can define their “trust” on the map data according totheir confidence level. The “trust” can be modeled using the maximaldeviation of one input point in the final output and can be considereddirectly in the method.

According to one embodiment, a first reference line representing atrajectory from a first location to a second location associated with anautonomous driving vehicle (ADV) is received. The first reference linewas generated from map data associated with the route from the firstlocation to the second location. The first reference line is segmentedinto a number of reference line segments. For each of the reference linesegments, a quintic polynomial function (also simply referred to as aquintic function) is defined to represent the corresponding referenceline segment. An objective function is determined based on the quinticpolynomial functions of the reference line segments. An optimization isthen performed on parameters or coefficients of the quintic polynomialfunctions in view of a set of constraints associated with the referenceline segments, such that an output of the objective function reachesminimum while the set of constraints are satisfied. A second referenceline is then generated based on the optimized parameters or coefficientsof the quintic polynomial functions of the objective function. Thesecond reference line is then utilized to plan the trajectory for theADV.

In one embodiment, the objective function represents a sum of alloutputs of the quintic polynomial functions of all reference linesegments. In a particular embodiment, the objective function isconfigured based on a sum of second order derivatives of the quinticpolynomial functions of the reference line segments. The coefficients ofa quintic polynomial function of each reference line segment aredetermined based on the reference line direction, curvature andcurvature change rate at the reference line's two terminals, and alength of the reference line segment, in view of the set of constraints.In one embodiment, the optimization on the parameters of the quinticpolynomial functions includes optimizing the coefficients of eachquintic polynomial function, such that the output of the quinticpolynomial functions have minimal curvature changes.

In one embodiment, the set of constraints further includes a conditionin which a first order derivative of a quintic polynomial function at astarting point of a reference line segment is similar to a curvature atthe starting point of the reference line segment. A first order of thequintic polynomial function at an ending point of the reference linesegment is the same or similar to a curvature at a starting point of anext reference line segment. In another embodiment, the set ofconstraints further includes a condition in which a second orderderivative of the quintic polynomial function at the starting point ofthe reference line segment is similar to a curvature change rate at thestarting point of the reference line segment. A second order derivativeof the quintic polynomial function at the ending point of the referenceline segment is the same or similar to a curvature change rate at thestarting point of the next reference line segment. The set ofconstraints further includes a condition in which a difference between aterminal point on the first reference line and a corresponding terminalpoint derived from the quintic polynomial function is below apredetermined threshold, where the threshold may be user configurable,e.g., dependent upon the confidence or trust level associated with thesensors of the ADV.

FIG. 1 is a block diagram illustrating an autonomous vehicle networkconfiguration according to one embodiment of the disclosure. Referringto FIG. 1, network configuration 100 includes autonomous vehicle 101that may be communicatively coupled to one or more servers 103-104 overa network 102. Although there is one autonomous vehicle shown, multipleautonomous vehicles can be coupled to each other and/or coupled toservers 103-104 over network 102. Network 102 may be any type ofnetworks such as a local area network (LAN), a wide area network (WAN)such as the Internet, a cellular network, a satellite network, or acombination thereof, wired or wireless. Server(s) 103-104 may be anykind of servers or a cluster of servers, such as Web or cloud servers,application servers, backend servers, or a combination thereof. Servers103-104 may be data analytics servers, content servers, trafficinformation servers, map and point of interest (MPOI) severs, orlocation servers, etc.

An autonomous vehicle refers to a vehicle that can be configured to inan autonomous mode in which the vehicle navigates through an environmentwith little or no input from a driver. Such an autonomous vehicle caninclude a sensor system having one or more sensors that are configuredto detect information about the environment in which the vehicleoperates. The vehicle and its associated controller(s) use the detectedinformation to navigate through the environment. Autonomous vehicle 101can operate in a manual mode, a full autonomous mode, or a partialautonomous mode.

In one embodiment, autonomous vehicle 101 includes, but is not limitedto, perception and planning system 110, vehicle control system 111,wireless communication system 112, user interface system 113,infotainment system 114, and sensor system 115. Autonomous vehicle 101may further include certain common components included in ordinaryvehicles, such as, an engine, wheels, steering wheel, transmission,etc., which may be controlled by vehicle control system 111 and/orperception and planning system 110 using a variety of communicationsignals and/or commands, such as, for example, acceleration signals orcommands, deceleration signals or commands, steering signals orcommands, braking signals or commands, etc.

Components 110-115 may be communicatively coupled to each other via aninterconnect, a bus, a network, or a combination thereof. For example,components 110-115 may be communicatively coupled to each other via acontroller area network (CAN) bus. A CAN bus is a vehicle bus standarddesigned to allow microcontrollers and devices to communicate with eachother in applications without a host computer. It is a message-basedprotocol, designed originally for multiplex electrical wiring withinautomobiles, but is also used in many other contexts.

Referring now to FIG. 2, in one embodiment, sensor system 115 includes,but it is not limited to, one or more cameras 211, global positioningsystem (GPS) unit 212, inertial measurement unit (IMU) 213, radar unit214, and a light detection and range (LIDAR) unit 215. GPS system 212may include a transceiver operable to provide information regarding theposition of the autonomous vehicle. IMU unit 213 may sense position andorientation changes of the autonomous vehicle based on inertialacceleration. Radar unit 214 may represent a system that utilizes radiosignals to sense objects within the local environment of the autonomousvehicle. In some embodiments, in addition to sensing objects, radar unit214 may additionally sense the speed and/or heading of the objects.LIDAR unit 215 may sense objects in the environment in which theautonomous vehicle is located using lasers. LIDAR unit 215 could includeone or more laser sources, a laser scanner, and one or more detectors,among other system components. Cameras 211 may include one or moredevices to capture images of the environment surrounding the autonomousvehicle. Cameras 211 may be still cameras and/or video cameras. A cameramay be mechanically movable, for example, by mounting the camera on arotating and/or tilting a platform.

Sensor system 115 may further include other sensors, such as, a sonarsensor, an infrared sensor, a steering sensor, a throttle sensor, abraking sensor, and an audio sensor (e.g., microphone). An audio sensormay be configured to capture sound from the environment surrounding theautonomous vehicle. A steering sensor may be configured to sense thesteering angle of a steering wheel, wheels of the vehicle, or acombination thereof. A throttle sensor and a braking sensor sense thethrottle position and braking position of the vehicle, respectively. Insome situations, a throttle sensor and a braking sensor may beintegrated as an integrated throttle/braking sensor.

In one embodiment, vehicle control system 111 includes, but is notlimited to, steering unit 201, throttle unit 202 (also referred to as anacceleration unit), and braking unit 203. Steering unit 201 is to adjustthe direction or heading of the vehicle. Throttle unit 202 is to controlthe speed of the motor or engine that in turn control the speed andacceleration of the vehicle. Braking unit 203 is to decelerate thevehicle by providing friction to slow the wheels or tires of thevehicle. Note that the components as shown in FIG. 2 may be implementedin hardware, software, or a combination thereof.

Referring back to FIG. 1, wireless communication system 112 is to allowcommunication between autonomous vehicle 101 and external systems, suchas devices, sensors, other vehicles, etc. For example, wirelesscommunication system 112 can wirelessly communicate with one or moredevices directly or via a communication network, such as servers 103-104over network 102. Wireless communication system 112 can use any cellularcommunication network or a wireless local area network (WLAN), e.g.,using WiFi to communicate with another component or system. Wirelesscommunication system 112 could communicate directly with a device (e.g.,a mobile device of a passenger, a display device, a speaker withinvehicle 101), for example, using an infrared link, Bluetooth, etc. Userinterface system 113 may be part of peripheral devices implementedwithin vehicle 101 including, for example, a keyword, a touch screendisplay device, a microphone, and a speaker, etc.

Some or all of the functions of autonomous vehicle 101 may be controlledor managed by perception and planning system 110, especially whenoperating in an autonomous driving mode. Perception and planning system110 includes the necessary hardware (e.g., processor(s), memory,storage) and software (e.g., operating system, planning and routingprograms) to receive information from sensor system 115, control system111, wireless communication system 112, and/or user interface system113, process the received information, plan a route or path from astarting point to a destination point, and then drive vehicle 101 basedon the planning and control information. Alternatively, perception andplanning system 110 may be integrated with vehicle control system 111.

For example, a user as a passenger may specify a starting location and adestination of a trip, for example, via a user interface. Perception andplanning system 110 obtains the trip related data. For example,perception and planning system 110 may obtain location and routeinformation from an MPOI server, which may be a part of servers 103-104.The location server provides location services and the MPOI serverprovides map services and the POIs of certain locations. Alternatively,such location and MPOI information may be cached locally in a persistentstorage device of perception and planning system 110.

While autonomous vehicle 101 is moving along the route, perception andplanning system 110 may also obtain real-time traffic information from atraffic information system or server (TIS). Note that servers 103-104may be operated by a third party entity. Alternatively, thefunctionalities of servers 103-104 may be integrated with perception andplanning system 110. Based on the real-time traffic information, MPOIinformation, and location information, as well as real-time localenvironment data detected or sensed by sensor system 115 (e.g.,obstacles, objects, nearby vehicles), perception and planning system 110can plan an optimal route and drive vehicle 101, for example, viacontrol system 111, according to the planned route to reach thespecified destination safely and efficiently.

Server 103 may be a data analytics system to perform data analyticsservices for a variety of clients. In one embodiment, data analyticssystem 103 includes data collector 121 and machine learning engine 122.Data collector 121 collects driving statistics 123 from a variety ofvehicles, either autonomous vehicles or regular vehicles driven by humandrivers. Driving statistics 123 include information indicating thedriving commands (e.g., throttle, brake, steering commands) issued andresponses of the vehicles (e.g., speeds, accelerations, decelerations,directions) captured by sensors of the vehicles at different points intime. Driving statistics 123 may further include information describingthe driving environments at different points in time, such as, forexample, routes (including starting and destination locations), MPOIs,road conditions, weather conditions, etc.

Based on driving statistics 123, machine learning engine 122 generatesor trains a set of rules, algorithms, and/or predictive models 124 for avariety of purposes. For example, a set of quintic polynomial functionsmay be selected and defined with initial coefficients or parameters.Furthermore, a set of constraints may also be defined based on thehardware characteristics such as sensors specification and specificvehicle designs, which may obtained from the driving statistics 123.

FIGS. 3A and 3B are block diagrams illustrating an example of aperception and planning system used with an autonomous vehicle accordingto one embodiment. System 300 may be implemented as a part of autonomousvehicle 101 of FIG. 1 including, but is not limited to, perception andplanning system 110, control system 111, and sensor system 115.Referring to FIGS. 3A-3B, perception and planning system 110 includes,but is not limited to, localization module 301, perception module 302,prediction module 303, decision module 304, planning module 305, controlmodule 306, and routing module 307.

Some or all of modules 301-307 may be implemented in software, hardware,or a combination thereof. For example, these modules may be installed inpersistent storage device 352, loaded into memory 351, and executed byone or more processors (not shown). Note that some or all of thesemodules may be communicatively coupled to or integrated with some or allmodules of vehicle control system 111 of FIG. 2. Some of modules 301-307may be integrated together as an integrated module.

Localization module 301 determines a current location of autonomousvehicle 300 (e.g., leveraging GPS unit 212) and manages any data relatedto a trip or route of a user. Localization module 301 (also referred toas a map and route module) manages any data related to a trip or routeof a user. A user may log in and specify a starting location and adestination of a trip, for example, via a user interface. Localizationmodule 301 communicates with other components of autonomous vehicle 300,such as map and route information 311, to obtain the trip related data.For example, localization module 301 may obtain location and routeinformation from a location server and a map and POI (MPOI) server. Alocation server provides location services and an MPOI server providesmap services and the POIs of certain locations, which may be cached aspart of map and route information 311. While autonomous vehicle 300 ismoving along the route, localization module 301 may also obtainreal-time traffic information from a traffic information system orserver.

Based on the sensor data provided by sensor system 115 and localizationinformation obtained by localization module 301, a perception of thesurrounding environment is determined by perception module 302. Theperception information may represent what an ordinary driver wouldperceive surrounding a vehicle in which the driver is driving. Theperception can include the lane configuration (e.g., straight or curvelanes), traffic light signals, a relative position of another vehicle, apedestrian, a building, crosswalk, or other traffic related signs (e.g.,stop signs, yield signs), etc., for example, in a form of an object.

Perception module 302 may include a computer vision system orfunctionalities of a computer vision system to process and analyzeimages captured by one or more cameras in order to identify objectsand/or features in the environment of autonomous vehicle. The objectscan include traffic signals, road way boundaries, other vehicles,pedestrians, and/or obstacles, etc. The computer vision system may usean object recognition algorithm, video tracking, and other computervision techniques. In some embodiments, the computer vision system canmap an environment, track objects, and estimate the speed of objects,etc. Perception module 302 can also detect objects based on othersensors data provided by other sensors such as a radar and/or LIDAR.

For each of the objects, prediction module 303 predicts what the objectwill behave under the circumstances. The prediction is performed basedon the perception data perceiving the driving environment at the pointin time in view of a set of map/rout information 311 and traffic rules312. For example, if the object is a vehicle at an opposing directionand the current driving environment includes an intersection, predictionmodule 303 will predict whether the vehicle will likely move straightforward or make a turn. If the perception data indicates that theintersection has no traffic light, prediction module 303 may predictthat the vehicle may have to fully stop prior to enter the intersection.If the perception data indicates that the vehicle is currently at aleft-turn only lane or a right-turn only lane, prediction module 303 maypredict that the vehicle will more likely make a left turn or right turnrespectively.

For each of the objects, decision module 304 makes a decision regardinghow to handle the object. For example, for a particular object (e.g.,another vehicle in a crossing route) as well as its metadata describingthe object (e.g., a speed, direction, turning angle), decision module304 decides how to encounter the object (e.g., overtake, yield, stop,pass). Decision module 304 may make such decisions according to a set ofrules such as traffic rules or driving rules 312, which may be stored inpersistent storage device 352.

Routing module 307 is configured to provide one or more routes or pathsfrom a starting point to a destination point. For a given trip from astart location to a destination location, for example, received from auser, routing module 307 obtains route and map information 311 anddetermines all possible routes or paths from the starting location toreach the destination location. Routing module 307 may generate areference line in a form of a topographic map for each of the routes itdetermines from the starting location to reach the destination location.A reference line refers to an ideal route or path without anyinterference from others such as other vehicles, obstacles, or trafficcondition. That is, if there is no other vehicle, pedestrians, orobstacles on the road, an ADV should exactly or closely follows thereference line. The topographic maps are then provided to decisionmodule 304 and/or planning module 305. Decision module 304 and/orplanning module 305 examine all of the possible routes to select andmodify one of the most optimal route in view of other data provided byother modules such as traffic conditions from localization module 301,driving environment perceived by perception module 302, and trafficcondition predicted by prediction module 303. The actual path or routefor controlling the ADV may be close to or different from the referenceline provided by routing module 307 dependent upon the specific drivingenvironment at the point in time.

Based on a decision for each of the objects perceived, planning module305 plans a path or route for the autonomous vehicle, as well as drivingparameters (e.g., distance, speed, and/or turning angle), using areference line provided by routing module 307 as a basis. That is, for agiven object, decision module 304 decides what to do with the object,while planning module 305 determines how to do it. For example, for agiven object, decision module 304 may decide to pass the object, whileplanning module 305 may determine whether to pass on the left side orright side of the object. Planning and control data is generated byplanning module 305 including information describing how vehicle 300would move in a next moving cycle (e.g., next route/path segment). Forexample, the planning and control data may instruct vehicle 300 to move10 meters at a speed of 30 mile per hour (mph), then change to a rightlane at the speed of 25 mph.

Based on the planning and control data, control module 306 controls anddrives the autonomous vehicle, by sending proper commands or signals tovehicle control system 111, according to a route or path defined by theplanning and control data. The planning and control data includesufficient information to drive the vehicle from a first point to asecond point of a route or path using appropriate vehicle settings ordriving parameters (e.g., throttle, braking, and turning commands) atdifferent points in time along the path or route.

In one embodiment, the planning phase is performed in a number ofplanning cycles, also referred to as command cycles, such as, forexample, in every time interval of 100 milliseconds (ms). For each ofthe planning cycles or command cycles, one or more control commands willbe issued based on the planning and control data. That is, for every 100ms, planning module 305 plans a next route segment or path segment, forexample, including a target position and the time required for the ADVto reach the target position. Alternatively, planning module 305 mayfurther specify the specific speed, direction, and/or steering angle,etc. In one embodiment, planning module 305 plans a route segment orpath segment for the next predetermined period of time such as 5seconds. For each planning cycle, planning module 305 plans a targetposition for the current cycle (e.g., next 5 seconds) based on a targetposition planned in a previous cycle. Control module 306 then generatesone or more control commands (e.g., throttle, brake, steering controlcommands) based on the planning and control data of the current cycle.

Note that decision module 304 and planning module 305 may be integratedas an integrated module. Decision module 304/planning module 305 mayinclude a navigation system or functionalities of a navigation system todetermine a driving path for the autonomous vehicle. For example, thenavigation system may determine a series of speeds and directionalheadings to effect movement of the autonomous vehicle along a path thatsubstantially avoids perceived obstacles while generally advancing theautonomous vehicle along a roadway-based path leading to an ultimatedestination. The destination may be set according to user inputs viauser interface system 113. The navigation system may update the drivingpath dynamically while the autonomous vehicle is in operation. Thenavigation system can incorporate data from a GPS system and one or moremaps so as to determine the driving path for the autonomous vehicle.

Decision module 304/planning module 305 may further include a collisionavoidance system or functionalities of a collision avoidance system toidentify, evaluate, and avoid or otherwise negotiate potential obstaclesin the environment of the autonomous vehicle. For example, the collisionavoidance system may effect changes in the navigation of the autonomousvehicle by operating one or more subsystems in control system 111 toundertake swerving maneuvers, turning maneuvers, braking maneuvers, etc.The collision avoidance system may automatically determine feasibleobstacle avoidance maneuvers on the basis of surrounding trafficpatterns, road conditions, etc. The collision avoidance system may beconfigured such that a swerving maneuver is not undertaken when othersensor systems detect vehicles, construction barriers, etc. in theregion adjacent the autonomous vehicle that would be swerved into. Thecollision avoidance system may automatically select the maneuver that isboth available and maximizes safety of occupants of the autonomousvehicle. The collision avoidance system may select an avoidance maneuverpredicted to cause the least amount of acceleration in a passenger cabinof the autonomous vehicle.

Routing module 307 can generate reference routes, for example, from mapinformation such as information of road segments, vehicular lanes ofroad segments, and distances from lanes to curb. For example, a road canbe divided into sections or segments {A, B, and C} to denote three roadsegments. Three lanes of road segment A can be enumerated {A1, A2, andA3}. A reference route is generated by generating reference points alongthe reference route. For example, for a vehicular lane, routing module307 can connect midpoints of two opposing curbs or extremities of thevehicular lane provided by a map data. Based on the midpoints andmachine learning data representing collected data points of vehiclespreviously driven on the vehicular lane at different points in time,routing module 307 can calculate the reference points by selecting asubset of the collected data points within a predetermined proximity ofthe vehicular lane and applying a smoothing function to the midpoints inview of the subset of collected data points.

Based on reference points or lane reference points, routing module 307may generate a reference line by interpolating the reference points suchthat the generated reference line is used as a reference line forcontrolling ADVs on the vehicular lane. In some embodiments, a referencepoints table and a road segments table representing the reference linesare downloaded in real-time to ADVs such that the ADVs can generatereference lines based on the ADVs' geographical location and drivingdirection. For example, in one embodiment, an ADV can generate areference line by requesting routing service for a path segment by apath segment identifier representing an upcoming road section aheadand/or based on the ADV's GPS location. Based on a path segmentidentifier, a routing service can return to the ADV reference pointstable containing reference points for all lanes of road segments ofinterest. ADV can look up reference points for a lane for a path segmentto generate a reference line for controlling the ADV on the vehicularlane.

However, in some situations, the reference line generated from the mapdata is not smooth enough that may cause uncomfortable to the riders orcontrol errors of the vehicle. Sometimes the reference line goingthrough a reference point is not smooth enough. In order to have asmooth enough reference line, the curvature before and after eachreference point should be close to each other. In addition, thecurvature change rate should be reduced.

According to one embodiment, a new constrained numerical optimizationmethod is utilized, for example, by planning module 305, which takes themap data in a format of a sequence of 2D points and generates a smoothand piecewise concatenated reference line with minimal curvaturechanges. Given a sequence of 2D points, the system first connectsconsecutive points using arbitrary quintic polynomial spiral paths. Byperturbing these piecewise paths, the optimization system finds a bestset of these paths that have the overall minimal curvature changes, andare smoothly connected at the joint points up to the third derivative,in an iterative fashion.

The quintic polynomial spiral paths are utilized as piecewise paths tosimplify the objective formulation. The objective of the optimization isto minimize the overall curvature changes along the reference line.However, it is extremely complex to formulate the objective if thepiecewise paths are defined in world frames (e.g., in Cartesian space).To solve the problem, spiral paths, i.e., the curve direction isfunction of curve length, are utilized as piecewise paths, and thereforethe objective can be easily formulated. The coordinates of the points inthe spiral path can be computed using numerical integration. Inaddition, users can define their “trust” on the map data according totheir confidence level. The “trust” can be modeled using the maximaldeviation of one input point in the final output and can be considereddirectly in the method.

FIG. 4 is a block diagram illustrating an example of a planning moduleaccording to one embodiment. Referring to FIG. 4, planning module 305includes, but is not limited to, a segmenter 401, a quintic functiongenerator 402, an object function generator 403, an optimizer 404, and areference line generator 405. These modules 401-405 may be implementedin software, hardware, or a combination thereof. Segmenter 401 isconfigure to segment a first reference line into a number of referenceline segments. For each of the reference line segments, quintic functiongenerator 402 is configured to define and generate a quintic polynomialfunction to represent the corresponding reference line segment.Objective function generator 403 is configured to generate an objectivefunction based of the quintic polynomial functions of the reference linesegments. The quintic polynomial functions and/or the objectivefunctions may be preconfigured and stored as a part of functions 314.Optimizer 404 is configured to perform an optimization on the objectivefunction, such that the objective function reaches minimum in view of aset of constraints, which are configured by a constraint generator ofplanning module 305 (not shown) as a part of constraints 313. Referenceline generator 405 is configured to generate a second reference linebased on the optimization, i.e., using the parameters or coefficients ofthe optimized objective function. One of the goals of the optimizationis to determine a new set of reference points representing the secondreference line that are close to the corresponding original referencepoints of the first reference line, while the curvature changes orchanging rates between the reference line segments are maintainedminimum. Less curvature change leads to a smoother reference line.

FIG. 5 is a diagram illustrating an example of a reference linegenerated based on map data. Referring to FIG. 5, according to oneembodiment, segmenter 401 segments the reference line 500 into a numberof reference line segments. Each reference line segment is terminated bytwo reference points. In this example, there are n reference points (x0,y0), (x1, y1), . . . , (xn, yn), referred to herein as reference linesegments 501-506. Each reference line segment is associated with asegment length s. For example, reference line segment between referencepoints (x0, y0) and (x1, y1) is associated with segment length s0. Thus,for n reference points, there are (n−1) reference line segments. Eachreference line segment is modeled using a separate quintic polynomialfunction.

For each of the reference line segments, quintic function generator 402generates a quintic polynomial function θ(s). Thus, there are at least(n−1) quintic polynomial functions θ0(s) to θn−1(s). In one embodiment,each quintic polynomial function represents a direction of a startingreference point of the corresponding reference line segment. Aderivative (e.g., the first order derivative) of the quintic polynomialfunction represents a curvature of the starting reference point of thereference line segment, K=dθ/ds. A second order derivative of thequintic polynomial function represents a curvature change or curvaturechange rate, dK/ds.

For the purpose of illustration, following terms are defined:

θ₀; starting direction

{dot over (θ)}₀: starting curvature, n, derivative w.r.t. curve length,i.e.,

$\frac{d\;\theta}{ds}$

{umlaut over (θ)}₀: starting curvature derivative, i.e.,

$\frac{d\;\kappa}{ds}$

θ₁: ending direction

{dot over (θ)}₁: ending curvature

{umlaut over (θ)}₁: ending curvature derivative

Δs: the curve length between the two ends

Each piecewise spiral path is decided by seven parameters: startingdirection (θ0), starting curvature (dθ0), starting curvature derivative(d2θ0), ending direction (θ1), ending curvature (dθ1), ending curvaturederivative (d2θ1) and the curve length between the starting and endingpoints (Δs). In one embodiment, a quintic polynomial function can bedefined as follows:θ_(i)(s)=a*s ⁵ +b*s ⁴ +c*s ³ +d*s ² +e*s+fand it satisfiesθ_(i)(0)=θ_(i){dot over (θ)}_(i)(0)={dot over (θ)}_(i){umlaut over (θ)}_(i)(0)={umlaut over (θ)}_(i)θ_(i)(Δs)=θ_(i+1){dot over (θ)}_(i)(Δs)={dot over (θ)}_(i+1){umlaut over (θ)}_(i+1)(Δs)={umlaut over (θ)}_(i+1)

Based on the above constraints, the optimization is performed on allquintic polynomial functions of all reference line segments, such thatthe output of a quintic polynomial function representing reference linesegment (i) at zero segment length should be the same as or similar to adirection at the starting reference point of the corresponding referenceline segment (i). A first order derivative of the quintic polynomialfunction should be the same as or similar to a curvature at the startingreference point of the reference line segment (i). A second orderderivative of the quintic polynomial function should be the same as orsimilar to a curvature change rate at the starting reference point ofthe reference line segment (i). Similarly, the output of a quinticpolynomial function representing reference line segment (i) at the fullsegment length (s) should be the same as or similar to a direction atthe starting reference point of the next reference line segment (i+1),which is the ending reference point of the current reference linesegment (i). A first order derivative of the quintic polynomial functionshould be the same as or similar to a curvature at the startingreference point of the next reference line segment (i+1). A second orderderivative of the quintic polynomial function should be the same as orsimilar to a curvature change rate at the starting reference point ofthe next reference line segment (i+1).

For example, for reference line segment 501 as shown in FIG. 5, anoutput of the corresponding quintic polynomial function θ(0) representsa direction or angle of starting point (x0, y0). θ(Δs0) represents adirection of ending point (x1, y1), where point (x1, y1) is also thestarting point of the next reference line segment 502. A first orderderivative of θ(0) represents a curvature at starting point (x0, y0) anda second order derivative of θ(0) represents a curvature change rate atending point (x1, y1). A first order derivative of θ(s0) represents acurvature of ending point (x1, y1) and a second order derivative ofθ(s0) represents a curvature change rate of ending point (x1, y1).

By substituting the above variables θ_(i), {dot over (θ)}_(i), {umlautover (θ)}_(i), θ_(i+1), {dot over (θ)}_(i+1), {umlaut over (θ)}_(i+1),Δs in, there will be six equations that can be utilized to solve thecoefficients of the quintic polynomial function a, b, c, d, e, and f.For example, as stated above, the direction at a given point can bedefined using the above quintic polynomial function:θ(s)=as ⁵ +bs ⁴ +cs ³ +ds ² +es+f

The first order derivative of the quintic function represents acurvature at the point of the path:dθ=5as ⁴+4bs ³+3cs ²+2ds+e

The second order derivative of the quintic function represents acurvature change rate at the point of the path:d ²θ=20as ³+12bs ²+6cs+2d

For a given spiral path or reference line segment, there are two pointsinvolved: a starting point and an ending point, where the direction,curvature, and curvature change rate of each point can be represented bythe above three equations respectively. Thus, there are a total of sixequations for each spiral path or reference line segment. These sixequations can be utilized to determine the coefficients a, b, c, d, e,and f of the corresponding quintic function.

When a spiral path is utilized to represent a curve between consecutivereference points in the Cartesian space, there is a need to build aconnection or bridge between the spiral path curve length and a positionin the Cartesian space. Given a spiral path θ_(i)(s) defined by {θ_(i),dθ_(i), d²θ_(i), θ_(i+1), d²θ_(i+1), d²θ_(i+1), Δs}, and path startingpoint p_(i)=(x_(i), y_(i)), we need to determine the coordinate of pointp=(x, y) given any s=[0, Δs]. In one embodiment, the coordinates of agiven point can be obtained based on the following formula:x=x _(i)+∫₀ ^(s) cos(θ_(i)(s))dsy=y _(i)+∫₀ ^(s) sin(θ_(i)(s))ds

When s=Δs, the ending coordinates pi+1 are obtained given curve θi andstarting coordinates pi=(xi, yi). The optimization of the quinticfunctions are performed such that the overall output of the quinticfunctions of the spiral paths reach minimum, while the above set ofconstraints are satisfied. In addition, the coordinates of the terminalpoint derived from the optimization is required to be within apredetermined range (e.g., tolerance, error margins) with respect to thecorresponding coordinates of the initial reference line. That is, thedifference between each optimized point and the corresponding point ofthe initial reference line should be within a predetermined threshold.

According to one embodiment, an objective function is defined based onthe quintic functions of all spiral paths. An optimization is performedon the input parameters of the quintic functions (e.g., θ_(i), {dot over(θ)}_(i), {umlaut over (θ)}_(i), θ_(i+1), {dot over (θ)}_(i+1), {umlautover (θ)}_(i+1), Δs) of the objective function, while the constraintsdescribed above are satisfied. In one embodiment, the objective functionrepresents a sum of all quintic functions associated with all referenceline segments, and the optimization is performed, such that the outputof the objective function reaches minimum while the above set ofconstraints are satisfied. The optimization is iteratively performed,the variables are modified, and the set of constraints are evaluated,until the output of the objective function in a current iteration issimilar to the output of the objective function in a previous iteration.The term of “similar” herein refers to the difference between theoutputs of two consecutive iterations is below a predeterminedthreshold.

In this approach, a reference line is modeled as a sequence of piecewisequintic spiral paths with two consecutive reference points connectedwith one spiral path, as shown in FIG. 5. The input points are allowedto slightly deviate from their original positions within a predeterminedboundary or boundaries, which may be defined or configured by a user.The boundaries model the confidence level of the sensor accuracy,handling labeling errors, etc., when generating the map data. In oneembodiment, the variables in the optimization are selected as follows,given n points p₀=(x ₀, y ₀), . . . , p_(n-1)=(x _(n-1), y _(n-1)):

θ₀ θ₁ θ₂ . . . θ_(n−2) θ_(n−1) {dot over (θ)}₀ {dot over (θ)}₁ {dot over(θ)}₂ . . . {dot over (θ)}_(n−2) {dot over (θ)}_(n−1) {umlaut over (θ)}₀{umlaut over (θ)}₁ {umlaut over (θ)}₂ . . . {umlaut over (θ)}_(n−2){umlaut over (θ)}_(n−1) Δs₀ Δs₁ . . . Δs_(n−2)

The smoothness of the reference line is modeled as the absolute value ofthe curvature change rate, i.e., a second order derivative of quinticfunction θ(s).

According to one embodiment, each of the reference line segment issegmented into a number of sub-segments. Each sub-segment represents apiecewise sub-path within the piecewise path of the reference linesegment. FIG. 6 is a diagram illustrating a segmentation of a referenceline segment, where the reference line segment is further segmented intom sub-segments. Each sub-segment is represented by the quintic functionof the same reference line segment. Thus, there are m intermediatepoints from one piecewise path as probing points. The goal is tominimize the quintic functions of the sub-segments. An objectivefunction is defined as a sum of the outputs of the quintic functions ofthe sub-segments of each of the reference line segments. In oneembodiment, an objective function is defined as follows:

$\sum\limits_{i = 0}^{n - 2}{\sum\limits_{j = 0}^{m - 1}{{\overset{¨}{\theta}}_{i}( s_{j} )}^{2}}$subject to the following point positional movement constraints:(x _(i) −x _(i))²+(y _(i) −y _(i))² ≤r _(i) ²

In one embodiment, the objective function represents a sum of square ofa second derivative of each quintic polynomial function. Coordinates (x_(i), y _(i)) represent the original position of input point pi, and rirepresents a boundary for point pi, which may be user configurable.Coordinates (xi, yi) are derived based on the integrals of thecorresponding quintic functions as described above. The new coordinatesderived from the optimization are utilized to form a new reference line,which can be utilized to control the ADV. FIG. 7 shows an originalreference line and an optimized reference line using at least a portionof the optimization described above.

FIG. 8 is a flow diagram illustrating an example of a process foroptimizing a reference line according to one embodiment. Process 800 maybe performed by processing logic which may include software, hardware,or a combination thereof. For example, process 800 may be performed byplanning module 305 of FIG. 4. Referring to FIG. 8, in operation 801,processing logic receives a first reference line that was generatedbased on map data. The first reference line represents a trajectory froma first location to a second location along which an ADV is supposed tofollow. In operation 802, processing logic segments the first referenceline into a number of reference line segments. Each reference linesegment is terminated by a starting reference point and an endingreference point. Each reference point is represented by a set ofproperties including, but are not limited to, a location of thereference point in a 2D Cartesian space (x, y) and a direction (θ). Thecurvature K at the reference point can be obtained based on a derivativeof direction (θ) and a curvature change rate can be obtained based on aderivative of curvature K.

For each of the reference line segments, in operation 803, processinglogic determines a quintic polynomial function to represent thecorresponding reference line segment. In operation 804, processing logicdetermines an objective function based on the quintic polynomialfunctions of the reference line segments. In operation 805, processinglogic performs an optimization on parameters of the quintic polynomialfunctions of the objective function in view of a set of constraints(e.g., constraints based on θ, dθ, d2θ, x, y), such that an output ofthe objective function reaches minimum while the set of constraints aresatisfied. In operation 706, a second reference line is generated basedon the optimized parameters of the quintic polynomial functions of theobjective function. The second reference line is utilized to control theADV.

In performing the optimization, the parameters (e.g., coefficients a, b,c, d, e, and f) of the quintic polynomial functions are iterativelyadjusted and optimized in a number of iterations, and the output of theobjective function is evaluated. The parameters are configured based onthe input points of each reference line segment, such as, x, y,direction, curvature, and curvature change rate. The goal is to optimizethe location (x, y), direction, curvature, and curvature change rate ofeach quintic polynomial function, such that the output of the objectivefunction reaches minimum. When the optimization reaches a predeterminedexiting condition, the process will stop and the latest set ofparameters will be obtained to generate the new reference line. In oneembodiment, when a difference between outputs of two consecutiveiterations of optimization is below a predetermined threshold, theiterative process stops. Alternatively, when a number of iterationsreaches a predetermined number, the process will stop.

Note that some or all of the components as shown and described above maybe implemented in software, hardware, or a combination thereof. Forexample, such components can be implemented as software installed andstored in a persistent storage device, which can be loaded and executedin a memory by a processor (not shown) to carry out the processes oroperations described throughout this application. Alternatively, suchcomponents can be implemented as executable code programmed or embeddedinto dedicated hardware such as an integrated circuit (e.g., anapplication specific IC or ASIC), a digital signal processor (DSP), or afield programmable gate array (FPGA), which can be accessed via acorresponding driver and/or operating system from an application.Furthermore, such components can be implemented as specific hardwarelogic in a processor or processor core as part of an instruction setaccessible by a software component via one or more specificinstructions.

FIG. 9 is a block diagram illustrating an example of a data processingsystem which may be used with one embodiment of the disclosure. Forexample, system 1500 may represent any of data processing systemsdescribed above performing any of the processes or methods describedabove, such as, for example, perception and planning system 110 or anyof servers 103-104 of FIG. 1. System 1500 can include many differentcomponents. These components can be implemented as integrated circuits(ICs), portions thereof, discrete electronic devices, or other modulesadapted to a circuit board such as a motherboard or add-in card of thecomputer system, or as components otherwise incorporated within achassis of the computer system.

Note also that system 1500 is intended to show a high level view of manycomponents of the computer system. However, it is to be understood thatadditional components may be present in certain implementations andfurthermore, different arrangement of the components shown may occur inother implementations. System 1500 may represent a desktop, a laptop, atablet, a server, a mobile phone, a media player, a personal digitalassistant (PDA), a Smartwatch, a personal communicator, a gaming device,a network router or hub, a wireless access point (AP) or repeater, aset-top box, or a combination thereof. Further, while only a singlemachine or system is illustrated, the term “machine” or “system” shallalso be taken to include any collection of machines or systems thatindividually or jointly execute a set (or multiple sets) of instructionsto perform any one or more of the methodologies discussed herein.

In one embodiment, system 1500 includes processor 1501, memory 1503, anddevices 1505-1508 connected via a bus or an interconnect 1510. Processor1501 may represent a single processor or multiple processors with asingle processor core or multiple processor cores included therein.Processor 1501 may represent one or more general-purpose processors suchas a microprocessor, a central processing unit (CPU), or the like. Moreparticularly, processor 1501 may be a complex instruction set computing(CISC) microprocessor, reduced instruction set computing (RISC)microprocessor, very long instruction word (VLIW) microprocessor, orprocessor implementing other instruction sets, or processorsimplementing a combination of instruction sets. Processor 1501 may alsobe one or more special-purpose processors such as an applicationspecific integrated circuit (ASIC), a cellular or baseband processor, afield programmable gate array (FPGA), a digital signal processor (DSP),a network processor, a graphics processor, a communications processor, acryptographic processor, a co-processor, an embedded processor, or anyother type of logic capable of processing instructions.

Processor 1501, which may be a low power multi-core processor socketsuch as an ultra-low voltage processor, may act as a main processingunit and central hub for communication with the various components ofthe system. Such processor can be implemented as a system on chip (SoC).Processor 1501 is configured to execute instructions for performing theoperations and steps discussed herein. System 1500 may further include agraphics interface that communicates with optional graphics subsystem1504, which may include a display controller, a graphics processor,and/or a display device.

Processor 1501 may communicate with memory 1503, which in one embodimentcan be implemented via multiple memory devices to provide for a givenamount of system memory. Memory 1503 may include one or more volatilestorage (or memory) devices such as random access memory (RAM), dynamicRAM (DRAM), synchronous DRAM (SDRAM), static RAM (SRAM), or other typesof storage devices. Memory 1503 may store information includingsequences of instructions that are executed by processor 1501, or anyother device. For example, executable code and/or data of a variety ofoperating systems, device drivers, firmware (e.g., input output basicsystem or BIOS), and/or applications can be loaded in memory 1503 andexecuted by processor 1501. An operating system can be any kind ofoperating systems, such as, for example, Robot Operating System (ROS),Windows® operating system from Microsoft®, Mac OS®/iOS® from Apple,Android® from Google®, LINUX, UNIX, or other real-time or embeddedoperating systems.

System 1500 may further include IO devices such as devices 1505-1508,including network interface device(s) 1505, optional input device(s)1506, and other optional IO device(s) 1507. Network interface device1505 may include a wireless transceiver and/or a network interface card(NIC). The wireless transceiver may be a WiFi transceiver, an infraredtransceiver, a Bluetooth transceiver, a WiMax transceiver, a wirelesscellular telephony transceiver, a satellite transceiver (e.g., a globalpositioning system (GPS) transceiver), or other radio frequency (RF)transceivers, or a combination thereof. The NIC may be an Ethernet card.

Input device(s) 1506 may include a mouse, a touch pad, a touch sensitivescreen (which may be integrated with display device 1504), a pointerdevice such as a stylus, and/or a keyboard (e.g., physical keyboard or avirtual keyboard displayed as part of a touch sensitive screen). Forexample, input device 1506 may include a touch screen controller coupledto a touch screen. The touch screen and touch screen controller can, forexample, detect contact and movement or break thereof using any of aplurality of touch sensitivity technologies, including but not limitedto capacitive, resistive, infrared, and surface acoustic wavetechnologies, as well as other proximity sensor arrays or other elementsfor determining one or more points of contact with the touch screen.

IO devices 1507 may include an audio device. An audio device may includea speaker and/or a microphone to facilitate voice-enabled functions,such as voice recognition, voice replication, digital recording, and/ortelephony functions. Other IO devices 1507 may further include universalserial bus (USB) port(s), parallel port(s), serial port(s), a printer, anetwork interface, a bus bridge (e.g., a PCI-PCI bridge), sensor(s)(e.g., a motion sensor such as an accelerometer, gyroscope, amagnetometer, a light sensor, compass, a proximity sensor, etc.), or acombination thereof. Devices 1507 may further include an imagingprocessing subsystem (e.g., a camera), which may include an opticalsensor, such as a charged coupled device (CCD) or a complementarymetal-oxide semiconductor (CMOS) optical sensor, utilized to facilitatecamera functions, such as recording photographs and video clips. Certainsensors may be coupled to interconnect 1510 via a sensor hub (notshown), while other devices such as a keyboard or thermal sensor may becontrolled by an embedded controller (not shown), dependent upon thespecific configuration or design of system 1500.

To provide for persistent storage of information such as data,applications, one or more operating systems and so forth, a mass storage(not shown) may also couple to processor 1501. In various embodiments,to enable a thinner and lighter system design as well as to improvesystem responsiveness, this mass storage may be implemented via a solidstate device (SSD). However in other embodiments, the mass storage mayprimarily be implemented using a hard disk drive (HDD) with a smalleramount of SSD storage to act as a SSD cache to enable non-volatilestorage of context state and other such information during power downevents so that a fast power up can occur on re-initiation of systemactivities. Also a flash device may be coupled to processor 1501, e.g.,via a serial peripheral interface (SPI). This flash device may providefor non-volatile storage of system software, including BIOS as well asother firmware of the system.

Storage device 1508 may include computer-accessible storage medium 1509(also known as a machine-readable storage medium or a computer-readablemedium) on which is stored one or more sets of instructions or software(e.g., module, unit, and/or logic 1528) embodying any one or more of themethodologies or functions described herein. Processingmodule/unit/logic 1528 may represent any of the components describedabove, such as, for example, planning module 305, control module 306.Processing module/unit/logic 1528 may also reside, completely or atleast partially, within memory 1503 and/or within processor 1501 duringexecution thereof by data processing system 1500, memory 1503 andprocessor 1501 also constituting machine-accessible storage media.Processing module/unit/logic 1528 may further be transmitted or receivedover a network via network interface device 1505.

Computer-readable storage medium 1509 may also be used to store the somesoftware functionalities described above persistently. Whilecomputer-readable storage medium 1509 is shown in an exemplaryembodiment to be a single medium, the term “computer-readable storagemedium” should be taken to include a single medium or multiple media(e.g., a centralized or distributed database, and/or associated cachesand servers) that store the one or more sets of instructions. The terms“computer-readable storage medium” shall also be taken to include anymedium that is capable of storing or encoding a set of instructions forexecution by the machine and that cause the machine to perform any oneor more of the methodologies of the present disclosure. The term“computer-readable storage medium” shall accordingly be taken toinclude, but not be limited to, solid-state memories, and optical andmagnetic media, or any other non-transitory machine-readable medium.

Processing module/unit/logic 1528, components and other featuresdescribed herein can be implemented as discrete hardware components orintegrated in the functionality of hardware components such as ASICS,FPGAs, DSPs or similar devices. In addition, processingmodule/unit/logic 1528 can be implemented as firmware or functionalcircuitry within hardware devices. Further, processing module/unit/logic1528 can be implemented in any combination hardware devices and softwarecomponents.

Note that while system 1500 is illustrated with various components of adata processing system, it is not intended to represent any particulararchitecture or manner of interconnecting the components; as suchdetails are not germane to embodiments of the present disclosure. Itwill also be appreciated that network computers, handheld computers,mobile phones, servers, and/or other data processing systems which havefewer components or perhaps more components may also be used withembodiments of the disclosure.

Some portions of the preceding detailed descriptions have been presentedin terms of algorithms and symbolic representations of operations ondata bits within a computer memory. These algorithmic descriptions andrepresentations are the ways used by those skilled in the dataprocessing arts to most effectively convey the substance of their workto others skilled in the art. An algorithm is here, and generally,conceived to be a self-consistent sequence of operations leading to adesired result. The operations are those requiring physicalmanipulations of physical quantities.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise as apparent from the above discussion, itis appreciated that throughout the description, discussions utilizingterms such as those set forth in the claims below, refer to the actionand processes of a computer system, or similar electronic computingdevice, that manipulates and transforms data represented as physical(electronic) quantities within the computer system's registers andmemories into other data similarly represented as physical quantitieswithin the computer system memories or registers or other suchinformation storage, transmission or display devices.

Embodiments of the disclosure also relate to an apparatus for performingthe operations herein. Such a computer program is stored in anon-transitory computer readable medium. A machine-readable mediumincludes any mechanism for storing information in a form readable by amachine (e.g., a computer). For example, a machine-readable (e.g.,computer-readable) medium includes a machine (e.g., a computer) readablestorage medium (e.g., read only memory (“ROM”), random access memory(“RAM”), magnetic disk storage media, optical storage media, flashmemory devices).

The processes or methods depicted in the preceding figures may beperformed by processing logic that comprises hardware (e.g. circuitry,dedicated logic, etc.), software (e.g., embodied on a non-transitorycomputer readable medium), or a combination of both. Although theprocesses or methods are described above in terms of some sequentialoperations, it should be appreciated that some of the operationsdescribed may be performed in a different order. Moreover, someoperations may be performed in parallel rather than sequentially.

Embodiments of the present disclosure are not described with referenceto any particular programming language. It will be appreciated that avariety of programming languages may be used to implement the teachingsof embodiments of the disclosure as described herein.

In the foregoing specification, embodiments of the disclosure have beendescribed with reference to specific exemplary embodiments thereof. Itwill be evident that various modifications may be made thereto withoutdeparting from the broader spirit and scope of the disclosure as setforth in the following claims. The specification and drawings are,accordingly, to be regarded in an illustrative sense rather than arestrictive sense.

What is claimed is:
 1. A computer-implemented method operating anautonomous driving vehicle, the method comprising: in response to afirst reference line representing a route from a first location to asecond location associated with an autonomous driving vehicle (ADV),segmenting the first reference line into a plurality of reference linesegments; for each of the reference line segments, determining a quinticpolynomial function to represent the reference line segment; determiningan objective function based on the quintic polynomial functions of thereference line segments; performing an optimization on parameters of thequintic polynomial functions in view of a set of constraints associatedwith the reference line segments, such that an output of the objectivefunction reaches minimum while the set of constraints are satisfied; andgenerating a second reference line based on the optimized parameters ofthe quintic polynomial functions of the objective function, wherein thesecond reference line is utilized as a reference line of the route tocontrol the ADV.
 2. The method of claim 1, wherein the objectivefunction represents a sum of at least a portion of derivatives of thequintic polynomial functions of the reference line segments.
 3. Themethod of claim 1, wherein coefficients of a quintic polynomial functionof each reference line segment are determined based on a location of theADV, a direction of the ADV, curvature of the ADV, and curvature changerate of the ADV associated with the reference line segment of the firstreference line.
 4. The method of claim 3, wherein performing anoptimization on the parameters of the quintic polynomial functionscomprises optimizing coefficients of each quintic polynomial function,such that an output of the quintic polynomial function at a startingpoint of the reference line segment is similar to a direction of the ADVat the starting point of the reference line segment and an output of thequintic polynomial function at an ending point of the reference linesegment is similar to a direction of the ADV at a starting point of anext reference line segment.
 5. The method of claim 4, wherein the setof constraints further comprises a condition in which a first orderderivative of the quintic polynomial function at the starting point ofthe reference line segment is similar to a curvature at the startingpoint of the reference line segment, and wherein a first orderderivative of the quintic polynomial function at the ending point of thereference line segment is similar to a curvature at the starting pointof the next reference line segment.
 6. The method of claim 4, whereinthe set of constraints further comprises a condition in which a secondorder derivative of the quintic polynomial function at the startingpoint of the reference line segment is similar to a curvature changerate at the starting point of the reference line segment, and wherein asecond order derivative of the quintic polynomial function at the endingpoint of the reference line segment is similar to a curvature changerate at the starting point of the next reference line segment.
 7. Themethod of claim 4, wherein the set of constraints comprises a conditionin which a difference between a location of the ADV on the firstreference line and a corresponding location of the ADV derived from thequintic polynomial function is below a predetermined threshold.
 8. Themethod of claim 1, wherein the optimization is iteratively performed onthe objective function until a difference between an output of theobjective function of a current iteration and an output of the objectivefunction of a previous iteration is below a predetermined threshold. 9.The method of claim 1, wherein performing an optimization comprises:segmenting a first reference line segment of the plurality of referenceline segments into a plurality of sub-segments; for each of the secondsub-segments, performing a second optimization using a first quinticpolynomial function associated with the first reference line segment;and summing outputs of the first quintic polynomial functionscorresponding to the sub-segments to represent the first reference linesegment.
 10. A non-transitory machine-readable medium havinginstructions stored therein, which when executed by a processor, causethe processor to perform operations, the operations comprising: inresponse to a first reference line representing a route from a firstlocation to a second location associated with an autonomous drivingvehicle (ADV), segmenting the first reference line into a plurality ofreference line segments; for each of the reference line segments,determining a quintic polynomial function to represent the referenceline segment; determining an objective function based on the quinticpolynomial functions of the reference line segments; performing anoptimization on parameters of the quintic polynomial functions in viewof a set of constraints associated with the reference line segments,such that an output of the objective function reaches minimum while theset of constraints are satisfied; and generating a second reference linebased on the optimized parameters of the quintic polynomial functions ofthe objective function, wherein the second reference line is utilized asa reference line of the route to control the ADV.
 11. Themachine-readable medium of claim 10, wherein the objective functionrepresents a sum of at least a portion of derivatives of the quinticpolynomial functions of the reference line segments.
 12. Themachine-readable medium of claim 10, wherein coefficients of a quinticpolynomial function of each reference line segment are determined basedon a location of the ADV, a direction of the ADV, curvature of the ADV,and curvature change rate of the ADV associated with the reference linesegment of the first reference line.
 13. The machine-readable medium ofclaim 12, wherein performing an optimization on the parameters of thequintic polynomial functions comprises optimizing coefficients of eachquintic polynomial function, such that an output of the quinticpolynomial function at a starting point of the reference line segment issimilar to a direction of the ADV at the starting point of the referenceline segment and an output of the quintic polynomial function at anending point of the reference line segment is similar to a direction ofthe ADV at a starting point of a next reference line segment.
 14. Themachine-readable medium of claim 13, wherein the set of constraintsfurther comprises a condition in which a first order derivative of thequintic polynomial function at the starting point of the reference linesegment is similar to a curvature at the starting point of the referenceline segment, and wherein a first order derivative of the quinticpolynomial function at the ending point of the reference line segment issimilar to a curvature at the starting point of the next reference linesegment.
 15. The machine-readable medium of claim 13, wherein the set ofconstraints further comprises a condition in which a second orderderivative of the quintic polynomial function at the starting point ofthe reference line segment is similar to a curvature change rate at thestarting point of the reference line segment, and wherein a second orderderivative of the quintic polynomial function at the ending point of thereference line segment is similar to a curvature change rate at thestarting point of the next reference line segment.
 16. Themachine-readable medium of claim 13, wherein the set of constraintscomprises a condition in which a difference between a location of theADV on the first reference line and a corresponding location of the ADVderived from the quintic polynomial function is below a predeterminedthreshold.
 17. The machine-readable medium of claim 10, wherein theoptimization is iteratively performed on the objective function until adifference between an output of the objective function of a currentiteration and an output of the objective function of a previousiteration is below a predetermined threshold.
 18. The machine-readablemedium of claim 10, wherein performing an optimization comprises:segmenting a first reference line segment of the plurality of referenceline segments into a plurality of sub-segments; for each of the secondsub-segments, performing a second optimization using a first quinticpolynomial function associated with the first reference line segment;and summing outputs of the first quintic polynomial functionscorresponding to the sub-segments to represent the first reference linesegment.
 19. A data processing system, comprising: a processor; and amemory coupled to the processor to store instructions, which whenexecuted by the processor, cause the processor to perform operations,the operations including in response to a first reference linerepresenting a route from a first location to a second locationassociated with an autonomous driving vehicle (ADV), segmenting thefirst reference line into a plurality of reference line segments, foreach of the reference line segments, determining a quintic polynomialfunction to represent the reference line segment, determining anobjective function based on the quintic polynomial functions of thereference line segments, performing an optimization on parameters of thequintic polynomial functions in view of a set of constraints associatedwith the reference line segments, such that an output of the objectivefunction reaches minimum while the set of constraints are satisfied, andgenerating a second reference line based on the optimized parameters ofthe quintic polynomial functions of the objective function, wherein thesecond reference line is utilized as a reference line of the route tocontrol the ADV.
 20. The system of claim 19, wherein the objectivefunction represents a sum of at least a portion of derivatives of thequintic polynomial functions of the reference line segments.
 21. Thesystem of claim 19, wherein coefficients of a quintic polynomialfunction of each reference line segment are determined based on alocation of the ADV, a direction of the ADV, curvature of the ADV, andcurvature change rate of the ADV associated with the reference linesegment of the first reference line.
 22. The system of claim 21, whereinperforming an optimization on the parameters of the quintic polynomialfunctions comprises optimizing coefficients of each quintic polynomialfunction, such that an output of the quintic polynomial function at astarting point of the reference line segment is similar to a directionof the ADV at the starting point of the reference line segment and anoutput of the quintic polynomial function at an ending point of thereference line segment is similar to a direction of the ADV at astarting point of a next reference line segment.